Journal of Hydrology 508 (2014) 418–429

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Journal of Hydrology

journal homepage: www.elsevier .com/locate / jhydrol

Long-term SPI drought forecasting in the Awash River Basin in Ethiopiausing wavelet neural network and wavelet support vector regressionmodels

0022-1694/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jhydrol.2013.10.052

⇑ Corresponding author. Tel.: +1 514 398 7786; fax: +1 514 398 8387.E-mail address: jan.adamowski@mcgill.ca (J. Adamowski).

A. Belayneh a, J. Adamowski a,⇑, B. Khalil a, B. Ozga-Zielinski b

a Department of Bioresource Engineering, Faculty of Agricultural and Environmental Sciences, McGill University, 21 111 Lakeshore, Ste Anne de Bellevue, Quebec H9X 3V9, Canadab Department of Environment Protection and Development, Environmental Engineering Faculty, Warsaw University of Technology, ul. Nowowiejska 20, 12 Warsaw 00-653, Poland

a r t i c l e i n f o s u m m a r y

Article history:Received 14 May 2013Received in revised form 29 October 2013Accepted 30 October 2013Available online 7 November 2013This manuscript was handled by GeoffSyme, Editor-in-Chief, with the assistance ofBellie Sivakumar , Associate Editor

Keywords:ANNSupport vector regressionSPIDrought forecastingWavelet transformsAfrica

Long-term drought forecasts can provide valuable information to help mitigate some of the consequencesof drought. Data driven models are suitable forecast tools due to their minimal information requirementsand rapid development times. This study compares the effectiveness of five data driven models for fore-casting long-term (6 and 12 months lead time) drought conditions in the Awash River Basin of Ethiopia.The Standard Precipitation Index (SPI 12 and SPI 24) was forecasted using a traditional stochastic model(ARIMA) and compared to machine learning techniques such as artificial neural networks (ANNs), andsupport vector regression (SVR). In addition to these three model types, wavelet transforms were usedto pre-process the inputs for ANN and SVR models to form WA-ANN and WA-SVR models; this is the firsttime that WA-SVR models have been explored and tested for long-term SPI forecasting. The performancesof all models were compared using RMSE, MAE, R2 and a measure of persistence. The forecast results indi-cate that the coupled wavelet neural network (WA-ANN) models were better than all the other models inthis study for forecasting SPI 12 and SPI 24 values over lead times of 6 and 12 months in the Awash RiverBasin.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Drought, which occurs when there is a deficit in precipitationcompared to the long-term average, has many impacts. Of all theextreme climate induced events, droughts have the most complexconsequences, mainly due to the difficulty in identifying theirinception and their end (Wilhite, 1993). In addition, droughts im-pact a wide range of geographic areas. Globally, 22% of the eco-nomic damage caused by natural disasters and 33% of thedamage in terms of the number of persons affected can be attrib-uted to drought (Keshavarz et al., 2013). The impacts of droughtare more severe in sub-Saharan Africa, where rain-fed agriculturecomprises 95% of all agriculture. This dependence of rain-fed agri-culture leaves sub-Saharan Africa vulnerable to the impacts ofdrought. For example, in 2009, poor rainfall led to increaseddroughts and an increase of 53 million food insecure people inthe region (Husak et al., 2013).

Due to a slow evolution in time, drought is often a phenomenonwhose consequences take a significant amount of time with re-spect to its inception to be perceived by the socio-economic sector

(Cancelliere et al., 2007b). This feature allows for the mitigation ofsome of the impacts of drought, provided there is an effective mon-itoring system to provide information to decision makers. Effectivemonitoring of droughts can significantly help early warning sys-tems. In sub-Saharan Africa, effective rainfall monitoring contrib-utes to the allocation of aid during periods of drought (Husaket al., 2013). An important aspect of drought monitoring and thedevelopment of an early warning system is the ability to effectivelyforecast future drought events. Forecasting future drought eventsin a region is very important for finding sustainable solutions towater management and risk assessment of drought occurrences(Bordi and Sutera, 2007).

Drought forecasts can be done using either physical/conceptualor data driven models. While physical/conceptual models are goodat providing insight into catchment processes, they have been crit-icised for being difficult to implement for forecasting applications,requiring many different types of data and resulting in models thatare overly complex (Beven, 2006). In contrast, data driven modelshave minimum information requirements, rapid developmenttimes, and have been found to be accurate in various hydrologicalforecasting applications (Adamowski, 2008).

Data driven stochastic models have traditionally been used fordrought forecasting. Autoregressive integrated moving average

A. Belayneh et al. / Journal of Hydrology 508 (2014) 418–429 419

models (ARIMA) (Mishra and Desai, 2005,2006; Mishra et al., 2007;Han et al., 2010) have been the most widely used stochastic modelsfor hydrologic drought forecasting. Stochastic models are linearmodels and are limited in their ability to forecast non-linear data.To effectively forecast non-linear data, researchers in the last twodecades have increasingly begun to utilize artificial neural net-works (ANNs) to forecast hydrological data. ANNs have been usedin a number of studies as a drought forecasting tool (Mishra andDesai, 2006; Morid et al., 2007; Bacanli et al., 2008; Barros andBowden, 2008; Cutore et al., 2009; Karamouz et al., 2009; Marjand Meijerink, 2011; Mishra and Nagarajan, 2012).

Along with ANN models, Support Vector Machines (SVMs) are amachine learning technique that has become increasingly popularin hydrologic forecasting. SVMs can be divided into two main tech-niques, the Support Vector Classification (SVC) and Support VectorRegression (SVR), which address problems of classification andregression, respectively (Gao et al., 2001). There are several studieswhere SVR was used in hydrological forecasting. Khan and Coulibaly(2006) found that a SVR model performed better than ANNs in3–12 month predictions of lake water levels. Kisi and Cimen(2009) used SVRs to estimate daily evaporation. A study by Belaynehand Adamowski (2012) used SVR models to forecast the SPI in theAwash River Basin. The research presented in the current papercomplements the Belayneh and Adamowski (2012) study byforecasting the SPI over a larger selection of stations in the samearea, and by coupling, for the first time, SVR models with wavelettransforms.

The ability of these machine learning techniques (i.e. ANNs andSVRs) to forecast non-stationary data is limited. To overcome thislimitation, wavelet analysis has begun to be explored in hydrologicforecasting. Wavelet transforms are often used as a data pre-pro-cessing tool in order to reveal aspects of a time series that othersignal processing techniques cannot. Wavelet analysis has been ap-plied to examine rainfall-runoff relationships in Karstic watersheds(Labat et al., 1999), to evaluate rainfall-runoff models (Lane, 2007),to forecast river flow (Adamowski, 2008; Adamowski and Sun,2010), to forecast groundwater levels (Adamowski and Chan,2011), to forecast urban water demand (Adamowski et al., 2012)and for the purposes of drought forecasting (Kim and Valdes,2003; Ozger et al., 2012; Mishra and Singh, 2012; Belayneh andAdamowski, 2012).

The main objective of the current study is to compare the effec-tiveness of machine learning methods (in this case the ANN andSVR methods) as well as machine learning methods pre-processedwith wavelet transforms (WA-ANN and WA-SVR models), for long-term drought forecasting in arid regions (in this case the AwashRiver Basin of Ethiopia). All these methods were compared to a tra-ditional stochastic method (ARIMA model), which was used forcomparative purposes (to compare the performance of the newermethods with a widely used traditional method). The standardizedprecipitation index (SPI), a meteorological drought index, was thedrought index forecasted in this study, as it is a good indicator ofthe variability of East African droughts (Ntale and Gan, 2003). SPI12 and SPI 24 were forecast for lead times of 6 and 12 months;SPI 12 and SPI 24 are good indicators of long-term drought condi-tions. The coupling of wavelet transforms with SVR models for thepurpose of forecasting the SPI has not been explored to date in theliterature.

2. The Standardized Precipitation Index

The Standardized Precipitation Index (SPI) was developed byMcKee et al. (1993). The SPI is a meteorological drought index asit is based solely on precipitation data. Two main advantages arisefrom the use of the SPI index. First, as the index is based on

precipitation alone its evaluation is relatively easy (Cacciamaniet al., 2007). Second, the index makes it possible to describedrought on multiple time scales (Tsakiris and Vangelis, 2004;Mishra and Desai, 2006; Cacciamani et al., 2007). The SPI can onlybe computed when a sufficiently long (at least 30 years) and possi-bly continuous time-series of monthly precipitation data is avail-able (Cacciamani et al., 2007). SPI calculation begins by selectinga suitable probability density function to describe the precipitationdata (Cacciamani et al., 2007). The cumulative probability of an ob-served precipitation amount is computed after an appropriate den-sity function is chosen. The inverse normal (Gaussian) function isthen applied to the probability (Cancelliere et al., 2007a). For eachrainfall gauge in this study the gamma distribution function wasselected to fit the rainfall data. Alternatively, a lognormal or anexponential distribution can be used to model the precipitation.In this paper, we followed Edossa et al. (2010) on selecting thegamma distribution function to fit the rainfall data. Detailed com-putation of the SPI can be found in Cacciamani et al. (2007).

The SPI is a z-score and represents an event departure from themean, expressed in standard deviation units. The SPI is a normal-ized index in time and space and this feature allows for the com-parison of SPI values among different locations. SPI values can becategorized according to classes (Cacciamani et al., 2007). Normalconditions are established from the aggregation of two classes:�1 < SPI < 0 (mild drought) and 0 6 SPI 6 1 (slightly wet). SPI val-ues are positive or negative for greater or less than mean precipi-tation, respectively. Variance from the mean is a probabilityindication of the severity of the flood or drought that can be usedfor risk assessment (Morid et al., 2006). The more negative the SPIvalue for a given location, the more severe the drought. The timeseries of the SPI can be used for drought monitoring by settingapplication-specific thresholds of the SPI for defining droughtbeginning and ending times. Accumulated values of the SPI canbe used to analyze drought severity. In this study, the SPI_SL_6program developed by the National Drought Mitigation Centre,University of Nebraska-Lincoln, was used to compute time seriesof drought indices (SPI) for each station in the basin and for eachmonth of the year at different time scales. A drought event occursat the time when the value of the SPI is continuously negative; theevent ends when the SPI becomes positive. Even though the SPI is ameteorological drought index, it can be used to interpret differentaspects of drought. This study only forecast SPI 12 and SPI 24,which are tied to long-term drought conditions, which is the focusof this study. This study was interested in providing informationabout drought conditions that affect streamflow, groundwater orother hydrological systems within the Awash River basin. ShorterSPI runs, such as SPI 3 and SPI 6, are representative of agriculturaldrought conditions, which are measured by a deficit in soil mois-ture content (Mishra and Desai, 2006).

3. Awash River Basin

In this study, the SPI was forecast in the Awash River Basin ofEthiopia (Fig. 1). Forecasts were made and compared for twelvestations within the basin. Drought is a common occurrence inthe Awash River Basin (Edossa et al., 2010), and with approxi-mately 90% of the population engaged in agricultural activitiesthe area is especially vulnerable to the effects of drought (Desalegnet al., 2006). The heavy dependence of the population on rain-fedagriculture has made the people and the country’s economy extre-mely vulnerable to the impacts of droughts. Current monthly andseasonal drought forecasts are done using the normalized differ-ence vegetation index (NDVI). While the NDVI is an effectivedrought index, it is sensitive to changes in vegetation and has lim-itations in areas where vegetation is minimal. Forecasts of SPI

Fig. 1. The Awash River Basin. Ministry of Water Resources, Ethiopia. Agricultural Water Management Information System. http://www.mowr.gov.et/AWMISET/images/Awash_agroecologyv3.pdf Accessed 06-June-2013.

420 A. Belayneh et al. / Journal of Hydrology 508 (2014) 418–429

in this case SPI 12 and SPI 24) are not dependent on vegetative cov-er and can be used as another tool for drought forecasts within thebasin and the country as a whole to complement the NDVIforecasts.

The mean annual rainfall of the basin varies from about1600 mm in the highlands to 160 mm in the northern point ofthe basin. The total amount of rainfall also varies greatly from yearto year, resulting in severe droughts in some years and flooding inothers. The total annual surface runoff in the Awash Basin amountsto some 4900 � 106 m3 (Edossa et al., 2010). Effective forecasts ofthe SPI can be used for mitigating the impacts of hydrologicaldrought that manifests as a result of rainfall shortages in the area.The climate of the Awash River Basin varies between a mild tem-perate climate in the Upper Awash sub-basin to a hot semi-arid cli-mate in both the Middle and Lower sub-basins. The Awash RiverBasin supports farming, from the growth of lowland crops suchas maize and sesame to pastoral farming practices. Rainfall recordsfrom 1970 to 2005 were used to generate SPI 12 and SPI 24 timeseries from each station. Descriptive statistics for precipitation atthe rainfall stations is shown in Table 1.

The normal ratio method, recommended by Linsley et al.(1988), was used to estimate the missing rainfall records at anystations that had incomplete precipitation records. With this meth-od, rain depths for missing data are estimated from observations atthree stations as close to, and as evenly spaced around the stationwith missing records, as possible. The distance matrix was

established for all rain gauge stations in the basin based on theirgeographic locations in order to assess the proximity of stationswith each other. All data sets were normalized using:

Xn ¼X0 � Xmin

Xmax � Xminð1Þ

where X0 and Xn represent the original and normalized data respec-tively, while Xmin and Xmax represent the minimum and maximumvalue among the original data.

4. Model development

4.1. ARIMA models

ARIMA models were developed based on the Box and Jenkinsapproach and consist of three steps: model identification, parame-terization and validation. The general non-seasonal ARIMA modelmay be written as (Box and Jenkins, 1976):

zt ¼hðBÞat

/ðBÞrdð2Þ

/B ¼ ð1� /tB� /2B2 � � � �/pBp ð3Þ

and

Table 1Descriptive Statistics of the Awash River Basin.

Basin Station Mean annualprecipitation(mm)

Max annualprecipitation(mm)

Standarddeviation(mm)

UpperAwashBasin

BantuLiben

91 647 111

Ginchi 97 376 90Sebeta 111 1566 172Ejersalele 67 355 75Ziquala 100 583 110

MiddleAwashBasin

Modjo 76 542 92Wolenchiti 76 836 95Gelemsso 77 448 75Dire Dawa 51 267 54

LowerAwashBasin

Eliwuha 44 374 57Dubti 87 449 89Bati 26 268 40

A. Belayneh et al. / Journal of Hydrology 508 (2014) 418–429 421

hB ¼ ð1� h1B� h2B2 � � � � hqBq ð4Þ

where zt is the observed time series and B is a back shift operator. /(B) and h(B) are polynomials of order p and q, respectively. The or-ders p and q are the order of non-seasonal auto-regression and theorder of non-seasonal moving average, respectively. Random errorsat are assumed to be independently and identically distributed witha mean of zero and a constant variance. rd describes the differenc-ing operation to data series to make the data series stationary and dis the number of regular differencing.

The first step in developing ARIMA models was determining thestationarity of a time series. To determine stationarity, the NUMxlExcel add-on was used. Once non-stationarity is removed the auto-correlation (ACF) and partial autocorrelation functions (PACF) wereused to determine the correlation structure of the data. Once thesignificant lags were determined using the ACF and PACF, differentcombinations were used to determine the optimal model structure.For instance, if the ACF and PACF for SPI 12 showed significant lagsat 5 and 2 lags respectively, different combinations for p and qwere used with intervals between 1 and 5 for p and 1 and 2 forq. The selection of ARIMA models was determined based on boththe accuracy and precision of models. The combinations that pro-vided the most accurate forecast models as measured by theMAE and the most precise models as measured by the RMSE werechosen. The details on the development of ARIMA models for SPItime series can be found in the works of Mishra and Desai (2005)and Mishra et al. (2007). For all ARIMA models, the data was par-titioned so that 90% of the data was a calibration set and 10% ofthe data was a validation set.

4.2. ANN models

The advantage of using ANNs is their parsimonious datarequirements, rapid execution time and ability to produce modelswhere the relationship between inputs and outputs are not fullyunderstood. The ANN models used in this study have a feed for-ward Multi-layer perceptron (MLP) architecture which was trainedwith the Levenberg–Marquardt (LM) back propagation algorithm.MLPs have often been used in hydrologic forecasting due to theirsimplicity. MLPs consist of an input layer, one or more hidden lay-ers, and an output layer (Kim and Valdes, 2003):

y0kðtÞ ¼ f0

Xm

j¼1

wkj � fn

XN

i¼1

wjixiðtÞ þ ðwj0Þ þwk0

" #ð5Þ

where N is the number of samples, m is the number of hidden neu-rons, xi(t) = the ith input variable at time step t; wji = weight that

connects the ith neuron in the input layer and the jth neuron inthe hidden layer; wj0 = bias for the jth hidden neuron; fn = activationfunction of the hidden neuron; wkj = weight that connects the jthneuron in the hidden layer and kth neuron in the output layer;wk0 = bias for the kth output neuron; f0 = activation function forthe output neuron; and y0kðtÞ is the forecasted kth output at timestep t (Kim and Valdes, 2003).

For ANN model development, the determination of the architec-ture of the model is very important. The optimal number of neu-rons in the input layer was determined by trial and error. As theSPI requires only precipitation for its computation it was the onlyinput used. The SPI was lagged to generate several neurons in theinput layer and the number of neurons that provided the lowestRMSE values was chosen as the appropriate number. Traditionally,the number of hidden neurons for ANN models is selected via atrial and error method. However a study by Wanas et al. (1998)empirically determined that the best performance of a neural net-work occurs when the number of hidden neurons is equal to log(N), where N is the number of training samples. Another study con-ducted by Mishra and Desai (2006) determined that the optimalnumber of hidden neurons is 2n + 1, where n is the number of in-put neurons. In this study, the optimal number of hidden neuronswas determined to be between log(N) and (2n + 1). For example, ifusing the method proposed by Wanas et al. (1998) gave a result of4 hidden neurons and using the method proposed by Mishra andDesai (2006) gave 7 hidden neurons, the optimal number of hiddenneurons was assumed to be between 4 and 7; thereafter the opti-mal number was chosen via trial and error. These two methodshelped establish an upper and lower bound for the number of hid-den neurons.

The ANN models used to forecast the SPI were recursive models.A recursive ANN model is similar to an ARIMA model in terms ofthe forecasting approach, and forecasts one time step ahead. Forsubsequent forecasts the network is applied recursively, usingthe previous predictions as inputs. Recursive ANN models havebeen shown to be effective for forecasts of the SPI for long leadtimes (e.g., Mishra and Nagarajan, 2012). In addition, preliminaryanalysis conducted for each station in our study indicated thatrecursive models were more accurate than direct multistep mod-els, and as such the recursive forecasting approach was used in thisstudy. For all the ANN models, 80% of the data was used to train themodels, while the remaining 20% of the data was divided into atesting and validation set with each set comprising 10% of the data.

4.3. SVR models

SVR models adhere to the structural risk minimization principleas opposed to the empirical risk minimization principle used byconventional neural networks (Vapnik, 1995). As a result, thesemodels reduce the generalization error as opposed to the trainingerror. With SVR, the purpose is to estimate a functional depen-dency f(~x) between a set of sampled points X ¼ f~x1;~x2; . . . ;~xng ta-ken from Rn and target values Y = {y1, y2, . . ., yn} with yi e R (theinput and target vectors (xi’s and yi’s) refer to the monthly recordsof the SPI index). Detailed descriptions of SVR model developmentcan be found in Cimen (2008).

All SVR models were created using the OnlineSVR software cre-ated by Parrella (2007), which can be used to build support vectormachines for regression. The data was partitioned into two sets: acalibration set and a validation set. 90% of the data was partitionedinto the calibration set while the final 10% of the data was used asthe validation set. Unlike neural networks the data can only be par-titioned into two sets with the calibration set being equivalent tothe training and testing sets found in neural networks. All inputsand outputs were standardized between 0 and 1.

Fig. 2. The SPI 12 time series at the Eliwuha station and the approximation timeseries at different decomposition levels. The first time series is the original signalfollowed by decompositions a level 1–8.

422 A. Belayneh et al. / Journal of Hydrology 508 (2014) 418–429

All SVR models used the non-linear radial basis function (RBF)kernel. As a result, each SVR model consisted of three parametersthat were selected: gamma (c), cost (C), and epsilon (e). The cparameter is a constant that reduces the model space and controlsthe complexity of the solution, while C is a positive constant that isa capacity control parameter, and e is the loss function thatdescribes the regression vector without all the input data (Kisiand Cimen, 2011). These three parameters were selected basedon a trial and error procedure. The combination of parameters thatproduced the lowest RMSE and MAE values for the calibration datasets were selected.

4.4. Wavelet decomposition

The wavelet transform is a mathematical tool that provides atime–frequency representation of a signal in the time domain(Partal and Kisi, 2007). In addition, wavelet analysis can often com-press or de-noise a signal (Kim and Valdes, 2003) and thus, is aneffective method for dealing with local discontinuities in a giventime series. The continuous wavelet transform (CWT) of a signalx(t) is defined as (Nason and Von Sachs, 1999):

Wðs; sÞ ¼ 1ffiffiffiffiffijsj

p Z 1

�1xðtÞw� t � s

s

� �dt ð6Þ

where s is the scale parameter; s is the translation, w is the motherwavelet and * corresponds to the complex conjugate (Kim and Val-des, 2003).

CWT is not often used for forecasting due to its complexity andlong computation times. Instead, the wavelet is discretized in fore-casting applications to simplify the numerical calculations. The dis-crete wavelet transform (DWT) requires less computation time andis simpler to implement (Nason and Von Sachs, 1999):

wj;kðtÞ ¼1ffiffiffiffiffiffiffisj

0j���r w

t � ks0sj0

sj0

!ð7Þ

where j and k are integers that control the scale and translationrespectively, while s0 > 1 is a fixed dilation step (Cannas et al.,2006) and s0 is a translation factor that depends on the aforemen-tioned dilation step.

One of the inherent limitations of using the DWT for forecastingapplications is that it is not shift invariant (i.e. if we change valuesat the beginning of our time series, all of the wavelet coefficientswill change). To overcome this problem, a redundant algorithm,known as the à trous algorithm, can be used and is given by(Mallat, 1998):

Ciþ1ðkÞ ¼Xþ1

l¼�1hðlÞciðkþ 2ilÞ ð8Þ

where h is the low pass filter and Ci+1(k) is the original time series.To extract the details, wi(k), that were eliminated in Eq. (8), thesmoothed version of the signal is subtracted from the coarser signalthat preceded it, given by (Murtagh et al., 2003):

wiðkÞ ¼ ci�1ðkÞ � ciðkÞ ð9Þ

where ci(k) is the approximation of the signal and ci�1(k) is the coar-ser signal. Each application of Eqs. (8) and (9) results in a smootherapproximation and extracts a higher level of detail. Finally, the non-symmetric Haar wavelet can be used as the low pass filter for the àtrous algorithm to prevent any future information from being usedduring the decomposition (Renaud et al., 2002).

The selection of the appropriate wavelet transform for an appli-cation requires a prior understanding of the attributes of the can-didate wavelet. The shift invariant property of the ‘a trous’ Haar

wavelet makes it the most suitable wavelet for forecasting applica-tions (Maheswaran and Khosa, 2012b), and this is why it was usedin this study. Furthermore, a study by Kim and Valdes (2003) foundthe ‘a trous’ wavelet to be more effective for forecasting studiesthan the Morlet or Daubechies wavelets. The aim of the ‘a trous’wavelet is to fill any gaps with redundant information that is ob-tained from the original series. The redundant information pro-vides a basis for enhanced forecasting accuracy (Maheswaranand Khosa, 2012a). The Haar wavelet, which is a low-pass filter,is concentrated over the narrowest support band, and thereforehas good localization properties. This attribute makes the Haarwavelet more suitable for dynamic time series where it is effectiveat detecting changes within the time series (Maheswaran andKhosa, 2012b). The ‘a trous’ wavelet is appropriate for forecastingdue to its localization capability in both the time and frequencydomains, and the Haar wavelet as a low-pass filter is appropriatefor detecting any changes that may occur within the 35 year SPIrecord in this study due to its localization properties as a resultof its energy being concentrated over a narrow support band.

When conducting wavelet analysis, the number of decomposi-tion levels that is appropriate for the data must be carefully se-lected. In this study, each SPI time series was decomposedbetween 1 and 8 levels. Fig. 2 depicts the SPI 12 time series ofthe Eliwuha station and the approximation series at differentdecomposition levels. The results were compared at all decompo-sition levels to determine the appropriate decomposition level.Fig. 2 indicates that the higher the level of decomposition, the lesslikely the transformed signal represents the original time series.Hence, the transformed times series was chosen after decomposingthe original time series to level three or level four. The results froma decomposition of level three or four provided the most accurateforecast results as measured by the performance measures used inthis study. Once a given time series was successfully decomposed,it was used as an input for either ANN or SVR models. Instead ofusing the original SPI data and its subsequent lags, a new wavelettransformed time series was used. After pre-processing, the gener-ation of ANN and SVR models, including data partition was done inexactly the same way as the ANN and SVR models without wavelettransforms.

4.5. Performance measures

The following measures of goodness of fit were used to evaluatethe forecast performance of all the aforementioned models:

Table 2The decompositions of the SPI 12 series at the Eliwuha station with the correlationand variation of these decompositions to the original SPI 12 series.

Decomposition level R2 RMSE

Level 1 0.8408 0.0742Level 2 0.8408 0.0742Level 3 0.9727 0.0412Level 4 0.9458 0.0490Level 5 0.8408 0.0742Level 6 0.7033 0.1068Level 7 0.6671 0.1300Level 8 0.6129 0.1446

A. Belayneh et al. / Journal of Hydrology 508 (2014) 418–429 423

The coefficient of determinationðR2Þ ¼PN

i¼1ðyi � yiÞ2PNi¼1ðyi � y

�Þ

2 ð10Þ

where y�¼ 1

N

XN

i¼1

yi ð11Þ

where y�

is the mean value taken over N, yi is the observed value, yi isthe forecasted value and N is the number of data points. The coeffi-cient of determination measures the degree of association amongthe observed and predicted values.

The Root Mean Squared ErrorðRMSEÞ ¼ffiffiffiffiffiffiffiffiSSEN

rð12Þ

where SSE is the sum of squared errors, and N is the number of sam-ples used. SSE is given by:

SSE ¼XN

i¼1

ðyi � yiÞ2 ð13Þ

with the variables already having been defined.

The Mean Absolute ErrorðMAEÞ ¼XN

i¼1

jyi � yijN

ð14Þ

The MAE is used to measure how close forecasted values are tothe observed values. It is the average of the absolute errors.

The results in this section were also compared via the persis-tence index (PERS)

PERS ¼ 1� SSESSEnaive

ð15Þ

where SSEnaive ¼Xðyi � yi�LÞ

2 ð16Þ

As mentioned above, SSE is the sum of squared errors. y1�L is theestimate from a persistence model that takes the last observation(at time 1 minus the lead time (L)) (Tiwari and Chatterjee, 2010).A value of PERS smaller or equal to 0 indicates that the model un-der study performs worse or no better than the easy to implementnaïve model. A PERS value of 1 is obtained when the model understudy provides exact estimates of observed values.

Table 3Model input structure for the Eliwuha station (6 months lead time).

Recursive order Input structure Target

1st step SPI(t�4), SPI(t�3), SPI(t�2), (SPI t�1), SPI (t) SPI(t+1)2nd step SPI(t�3), SPI(t�2), SPI (t�1), SPI (t), SPI(t+1) SPI(t+2)3rd step SPI(t�2), SPI(t�1), SPI(t), (SPI t+1), SPI (t+2) SPI(t+3)4th step SPI(t�1), SPI(t), SPI (t+1), SPI (t+2), SPI(t+3) SPI(t+4)5th step SPI(t), SPI(t+1), SPI(t+2), (SPI t+3), SPI (t+4) SPI(t+5)Test step SPI(t+1), SPI(t+3), SPI (t+4), SPI (t+4), SPI(t+5) SPI(t+6)

5. Results and discussion

In this study, the proposed forecast models for SPI 12 and SPI 24are presented for forecast lead times of 6 and 12 months. A SPI 12forecast of 6 months lead time represents a 6 month warning timefor SPI 12, and a 12 month lead time represents a 12 month warn-ing time and shows the variation in precipitation from year to year.Table 2 shows the inputs used for the proposed data driven modelsat the Eliwuha station (6 months lead time). Table 2 shows how themodels are applied recursively to reach the final target of a forecastof 6 months lead time. The table is applicable for the input struc-ture of both SPI 12 and SPI 24 (6 month lead time). The perfor-mance results of the proposed models for each station arepresented in Table 3 through Table 6. As mentioned earlier, modelsthat have a persistence index between 0 and 1 perform better thana naïve model. All the data driven models had a persistence indexgreater than 0. ARIMA models had a PERS of 0.36, ANN models hada PERS of 0.46, SVR models had a PERS of 0.41, WA-ANN models hada PERS of 0.58 and WA-SVR models had a PERS of 0.55 respectively.The results presented are based on the validation data sets. Table 7shows the performance results for the training/calibration set forSPI 12 forecasts (6 months lead time) at the Eliwuha station. Thetable shows that the forecast accuracy shown in the validation sets

is consistent with the results shown in the training or calibrationsets (see Table 8).

The models were forecast one time step ahead and the subse-quent result was used as an input in another model and forecastone time step ahead. The lead time in this study refers to theamount of time between the original time series and the final pre-dicted time series. The final output time series was either 6 or12 months ahead of the original time series. For each rainfall sta-tion, forecasts of SPI 12 and SPI 24 were made for 6 and 12 monthslead times. These forecasts were made using the five model typesoutlined above. The results presented in the following sectionsare from forecasts of SPI 12 (6 months lead time) at the Eliwuhastation. Only these results were presented in detail as it wouldbe very difficult to present all the results from each station in de-tail. The forecast results for all the stations are presented in Tables3–6, but these are not presented in detail.

5.1. ARIMA model results

The parameters for the ARIMA models were selected based onthe ACF and PACF of the time series in question. Once the signifi-cant lags were determined from the ACF and PACF, ARIMA modelswith different combinations were developed and the model thathad the lowest RMSE and MAE value was chosen. Figs. 3a and 3bare ACF and PACF figures for the Eliwuha station. The autocorrela-tion of the time series is significant for lags greater than 10 inFig. 3a; however no lag greater than 5 was selected for the purposeof parsimony. For this station a combination of parameters from 1to 5 were tested for p, while a value of 1 was tested for q. The com-bination that provided the lowest RMSE and MAE values was cho-sen as the model parameters. The results from the ARIMA modelsas shown in Tables 3 and 5 are significantly less accurate thanthe forecast results of the other model types (likely because ARIMAmodels are linear models).

5.2. ANN models

Fig. 4 provides the ANN model results at the Eliwuha station forSPI 12 at 6 months lead time. Fig. 4 indicates that the model hasgood generalization ability for SPI 12 and very little time shift erroras the extreme events for the predicted values correspond to theextreme values of the observed values. With respective extremedrought or extreme precipitation, the model does underestimate

Table 4The best ARIMA, ANN and SVR models for 6 and 12 month forecasts of SPI 12. Column 3 is the ANN architecture detailing the number of nodes in the input, hidden and outputlayers respectively. In column 11 the parameters of the SVR models are given.

Basin Station ANN models R2 RMSE MAE ARIMA (p,d,q) R2 RMSE MAE SVR (c,C,e) R2 RMSE MAE

6 Month lead timeUpper Bantu Liben 5-4-1 0.7013 0.3737 0.3051 (5,0,0) 0.5912 0.8757 0.7714 0.4, 99, 0.008 0.7343 0.2427 0.2063

Ginchi 5-4-1 0.7120 0.3834 0.3592 (5,1,1) 0.5391 0.8851 0.7459 0.4, 94, 0.008 0.7028 0.2535 0.1984Sebeta 5-4-1 0.6993 0.3784 0.3516 (4,0,0) 0.5827 0.8789 0.7407 0.4, 96, 0.008 0.7320 0.2805 0.2007Ejersalele 5-4-1 0.7103 0.3751 0.3458 (3,1,0) 0.5261 0.8846 0.7539 0.5, 90, 0.006 0.7127 0.2997 0.1984Ziquala 6-4-1 0.7201 0.3765 0.3271 (4,0,0) 0.5713 0.8623 0.7436 0.3, 89, 0.005 0.7382 0.2690 0.2052

Middle Modjo 5-4-1 0.7064 0.3673 0.3281 (3,110) 0.5329 0.8600 0.7333 0.6, 88, 0.008 0.7326 0.2917 0.2044Wolenchiti 6-4-1 0.7139 0.3722 0.3481 (5,0,0) 0.5537 0.8665 0.7388 0.9, 90, 0.008 0.7044 0.2884 0.1987Gelemsso 5-4-1 0.7045 0.3619 0.3581 (4,0,0) 0.5572 0.8751 0.7459 0.8, 91, 0.007 0.7150 0.2891 0.2147Dire Dawa 5-4-1 0.7123 0.3781 0.3440 (5,0,1) 0.5928 0.8731 0.7443 0.4, 92, 0.005 0.7329 0.2838 0.1885

Lower Dubti 6-4-1 0.7077 0.3409 0.3103 (5,0,0) 0.5472 0.8928 0.7607 0.8, 93, 0.008 0.7346 0.3054 0.1851Eliwuha 5-4-1 0.7565 0.3296 0.3019 (4,0,1) 0.5534 0.8857 0.7798 0.8, 95, 0.008 0.7653 0.3136 0.1953Bati 6-4-1 0.7210 0.3434 0.3097 (5,0,0) 0.5237 0.8928 0.7940 0.5, 87, 0.009 0.7547 0.2831 0.2162

12 Month lead timeUpper Bantu Liben 5-4-1 0.5129 0.4120 0.3742 (4,0,0) 0.4421 0.9556 0.7577 0.4, 90, 0.01 0.6087 0.3723 0.2582

Ginchi 6-4-1 0.5346 0.4309 0.3781 (4,0,1) 0.4472 0.9015 0.7343 0.5, 91, 0.007 0.6078 0.3794 0.2352Sebeta 5-4-1 0.5456 0.4456 0.3981 (5,0,0) 0.4638 0.9123 0.7295 0.6, 97, 0.003 0.6123 0.3912 0.2807Ejersalele 6-4-1 0.5422 0.4021 0.3448 (5,0,0) 0.4537 0.9286 0.7416 0.6, 100, 0.01 0.6078 0.3466 0.2051Ziquala 7-4-1 0.5437 0.4358 0.3891 (4,0,1) 0.4682 0.9526 0.7321 0.8, 99, 0.03 0.6234 0.3556 0.2599

Middle Modjo 6-4-1 0.5273 0.3996 0.3568 (4,1,0) 0.4572 0.9725 0.7755 0.5, 96, 0.008 0.6350 0.3482 0.2034Wolenchiti 7-4-1 0.5358 0.4180 0.3689 (3,0,0) 0.4589 0.9545 0.7785 0.8, 96, 0.008 0.6267 0.3114 0.1963Gelemsso 5-4-1 0.5441 0.4322 0.3889 (3,0,1) 0.4578 0.9592 0.7752 0.6, 94, 0.009 0.6290 0.3300 0.2115Dire Dawa 5-4-1 0.5291 0.3900 0.3770 (3,0,0) 0.4280 0.9678 0.7690 0.5, 96, 0.008 0.6443 0.3466 0.2016

Lower Dubti 6-4-1 0.5127 0.3976 0.3782 (2,0,2) 0.4627 0.9285 0.7904 0.6, 96, 0.004 0.6239 0.3359 0.2212Eliwuha 4-4-1 0.5371 0.4304 0.3623 (5,0,0) 0.4632 0.9204 0.7837 0.8, 94, 0.008 0.6219 0.3087 0.1958Bati 7-4-1 0.5230 0.4032 0.3703 (4,0,0) 0.4547 0.9890 0.7837 0.5, 96, 0.008 0.6387 0.3783 0.2426

Table 5The best WA-ANN and WA-SVR models for 6 and 12 month forecasts of SPI 12. Column 3 is the ANN architecture detailing the number of nodes in the input, hidden and outputlayers respectively. In column 7 the parameters of the SVR models are given.

Basin Station WA-ANN R2 RMSE MAE WA-SVR R2 RMSE MAE

6 Month lead timeUpper Bantu Liben 5-6-1 0.8696 0.2023 0.1933 0.4, 99, 0.008 0.8507 0.2409 0.1934

Ginchi 5-5-1 0.8276 0.2095 0.1831 0.4, 94, 0.008 0.8144 0.2314 0.2136Sebeta 5-5-1 0.8815 0.2013 0.1833 0.4, 96, 0.008 0.8380 0.2343 0.2214Ejersalele 7-5-1 0.9090 0.2066 0.1821 0.5, 90, 0.006 0.8363 0.2221 0.2054Ziquala 6-5-1 0.8616 0.2057 0.1830 0.3, 89, 0.005 0.8330 0.2413 0.2138

Middle Modjo 5-4-1 0.8953 0.2083 0.1828 0.6, 88, 0.008 0.8732 0.2245 0.2054Wolenchiti 7-4-1 0.9332 0.2015 0.1892 0.9, 90, 0.008 0.8644 0.2518 0.2210Gelemsso 6-5-1 0.9204 0.2000 0.1845 0.8, 91, 0.007 0.8726 0.2167 0.2017Dire Dawa 7-6-1 0.9129 0.2001 0.1928 0.4, 92, 0.005 0.8968 0.2212 0.2036

Lower Dubti 4-4-1 0.9231 0.2060 0.1847 0.8, 93, 0.008 0.8640 0.2185 0.2084Eliwuha 5-4-1 0.9326 0.2088 0.1804 0.8, 95, 0.008 0.8671 0.2440 0.2213Bati 6-4-1 0.9005 0.2183 0.1997 0.5, 87, 0.009 0.8441 0.2467 0.2341

12 Month lead timeUpper Bantu Liben 5-6-1 0.8034 0.2235 0.2115 0.4, 90, 0.01 0.7535 0.2484 0.2228

Ginchi 6-5-1 0.8261 0.2416 0.2128 0.5, 91, 0.007 0.7533 0.2455 0.2030Sebeta 5-5-1 0.8049 0.2314 0.2126 0.6, 97, 0.003 0.7148 0.2734 0.2622Ejersalele 8-6-1 0.8162 0.2208 0.2128 0.6, 100, 0.01 0.7342 0.2645 0.2406Ziquala 7-5-1 0.8300 0.2206 0.2128 0.8, 99, 0.03 0.7604 0.2922 0.2711

Middle Modjo 6-4-1 0.8292 0.2334 0.2242 0.5, 96, 0.008 0.7643 0.2645 0.2449Wolenchiti 8-5-1 0.8046 0.2365 0.2247 0.8, 96, 0.008 0.7843 0.2817 0.2733Gelemsso 7-6-1 0.8272 0.2354 0.2216 0.6, 94, 0.009 0.7721 0.2996 0.2717Dire Dawa 8-6-1 0.8219 0.2362 0.2117 0.5, 96, 0.008 0.7813 0.2674 0.2241

Lower Dubti 5-5-1 0.8549 0.2406 0.2052 0.6, 96, 0.004 0.7443 0.2745 0.2620Eliwuha 6-4-1 0.8473 0.2719 0.2534 0.8, 94, 0.008 0.7641 0.3012 0.2639Bati 8-4-1 0.8437 0.2350 0.2248 0.5, 96, 0.008 0.7134 0.2611 0.2418

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some instances where the observed SPI value corresponds to ex-treme conditions (�2 and 2) respectively. Fig. 5 is a scatter plotof the observed and ANN forecast results for the Eliwuha station.The scatter plot in Fig. 5 shows several points significantly belowthe trend line indicating a certain level of underestimation in theANN model results. The proposed ANN model from the Eliwuhastation had an R2 of 0.7564, an RMSE of 0.3296 and an MAE of0.3019, respectively. The R2 values of 0.7564 shows a good correla-tion between observed and predicted results at 6-months leadtime.

5.3. WA-ANN models

The results of all the proposed WA-ANN models can be found inTable 4 for both forecasts of 6 and 12 months lead time. The fore-cast results of WA-ANN models are more accurate than ANN mod-els according to the performance measures used. The use ofwavelets as a pre-processing tool resulted in more accurate andprecise models as seen in Tables 4 and 6. These model results havea higher level of correlation between the observed and predictedtime series and the RMSE and MAE values are lower compared to

Table 6The best ARIMA, ANN and SVR models for 6 and 12 month forecasts of SPI 24. Column 3 is the ANN architecture detailing the number of nodes in the input, hidden and outputlayers respectively. In column 11 the parameters of the SVR models are given.

Basin Station ANN models R2 RMSE MAE ARIMA (p,d,q) R2 RMSE MAE SVR (c,C,e) R2 RMSE MAE

6 Month lead timeUpper Bantu 4-4-1 0.7832 0.2775 0.2404 (5,1,0) 0.6486 0.5867 0.5735 0.8, 93, 0.08 0.7754 0.3192 0.2967

Liben 5-4-1 0.7949 0.3302 0.3238 (4,1,0) 0.6302 0.5853 0.5707 0.8, 94, 0.06 0.7581 0.3027 0.2883Ginchi 5-4-1 0.7682 0.3421 0.3325 (5,0,1) 0.6682 0.5844 0.5688 0.9, 93, 0.08 0.7961 0.3338 0.2991Sebeta 6-4-1 0.7881 0.3347 0.3131 (5,1,0) 0.6427 0.5832 0.5665 0.8, 93, 0.08 0.7515 0.3546 0.3029Ejersalele 4-4-1 0.7947 0.3619 0.3421 (5,0,1) 0.6362 0.5822 0.5644 0.5, 99, 0.05 0.7862 0.2627 0.2534Ziquala

Middle Modjo 4-4-1 0.7915 0.2836 0.2629 (5,0,0) 0.6526 0.6046 0.5421 0.7, 92, 0.06 0.7637 0.3115 0.2951Wolenchiti 4-4-1 0.7844 0.3302 0.3026 (4,0,1) 0.5721 0.5927 0.5721 0.6, 94, 0.08 0.7619 0.3143 0.3065Gelemsso 5-4-1 0.7916 0.2262 0.2202 (5,0,0) 0.6676 0.5821 0.5626 0.45, 96, 0.01 0.7738 0.3498 0.3431Dire Dawa 5-4-1 0.8042 0.2662 0.2632 (3,1,1) 0.6742 0.5780 0.5581 0.4, 89, 0.03 0.7887 0.2933 0.2788

Lower Dubti 4-4-1 0.8041 0.3397 0.3187 (5,0,0) 0.6248 0.5819 0.5355 0.4, 94, 0.07 0.7983 0.3141 0.2874Eliwuha 5-4-1 0.7965 0.3129 0.3017 (5,0,0) 0.6574 0.5827 0.5282 0.5, 97, 0.06 0.7831 0.3149 0.2932Bati 5-4-1 0.7914 0.2786 0.2645 (5,1,0) 0.6340 0.5595 0.5295 0.8, 98, 0.05 0.7681 0.2958 0.2804

12 Month lead timeUpper Bantu 5-4-1 0.7122 0.3545 0.3422 (4,1,1) 0.5442 0.7470 0.6946 0.55, 88, 0.08 0.7259 0.3256 0.3179

Liben 6-4-1 0.7294 0.3620 0.3467 (5,1,0) 0.5078 0.7414 0.6379 0.65, 96, 0.08 0.7219 0.3282 0.3074Ginchi 6-4-1 0.7164 0.3632 0.3474 (5,010) 0.5939 0.7377 0.6200 0.85, 99, 0.06 0.7083 0.3387 0.3188Sebeta 7-4-1 0.7231 0.3640 0.3493 (5,1,0) 0.5025 0.7330 0.5876 0.8, 88, 0.09 0.7296 0.3667 0.3594Ejersalele 5-4-1 0.7017 0.3692 0.3508 (5,0,1) 0.5145 0.7288 0.5804 0.6, 91, 0.06 0.7139 0.3786 0.3683Ziquala

Middle Modjo 5-4-1 0.7129 0.3816 0.3710 (4,0,1) 0.4780 0.8637 0.7777 0.6, 91, 0.05 0.7233 0.3783 0.3684Wolenchiti 5-4-1 0.7064 0.3705 0.3657 (5,0,0) 0.4471 0.8762 0.8186 0.45, 100, 0.09 0.7235 0.3630 0.3529Gelemsso 6-4-1 0.7215 0.3534 0.3290 (4,1,1) 0.5659 0.8889 0.8300 0.6, 98, 0.08 0.7242 0.3768 0.3710Dire Dawa 6-4-1 0.7146 0.3412 0.3148 (5,1,0) 0.5216 0.9035 0.7709 0.65, 92, 0.05 0.7023 0.3687 0.3433

Lower Dubti 5-4-1 0.7179 0.3716 0.3580 (5,0,0) 0.5158 0.8854 0.7244 0.5, 88, 0.09 0.7253 0.3398 0.3158Eliwuha 6-4-1 0.7189 0.3715 0.3471 (4,0,1) 0.4265 0.8643 0.7275 0.25, 100, 0.1 0.7018 0.3420 0.3261Bati 6-4-1 0.7136 0.3708 0.3600 (5,1,0) 0.4915 0.8312 0.7729 0.88, 95, 0.07 0.7061 0.3387 0.2916

Table 7The best WA-ANN and WA-SVR models for 6 and 12 month forecasts of SPI 24. Column 3 is the ANN architecture detailing the number of nodes in the input, hidden and outputlayers respectively. In column 7 the parameters of the SVR models are given.

Basin Station WA-ANN R2 RMSE MAE WA-SVR R2 RMSE MAE

6 Month lead timeUpper Bantu Liben 5-6-1 0.9665 0.1968 0.1803 0.8, 93, 0.08 0.8832 0.2461 0.2108

Ginchi 5-5-1 0.9254 0.2850 0.2671 0.8, 94, 0.06 0.8740 0.2475 0.2148Sebeta 5-5-1 0.8864 0.1821 0.1723 0.9, 93, 0.08 0.8742 0.2581 0.2331Ejersalele 7-5-1 0.8791 0.1778 0.1632 0.8, 93, 0.08 0.8683 0.2287 0.2023Ziquala 6-5-1 0.8978 0.2546 0.2395 0.5, 99, 0.05 0.8869 0.2192 0.2133

Middle Modjo 5-4-1 0.9166 0.2561 0.2481 0.7, 92, 0.06 0.8938 0.2407 0.2281Wolenchiti 7-4-1 0.9014 0.2115 0.2049 0.6, 94, 0.08 0.8892 0.2218 0.2106Gelemsso 6-5-1 0.9407 0.2258 0.2054 0.45, 96, 0.01 0.8935 0.2773 0.2694Dire Dawa 7-6-1 0.9215 0.2335 0.2149 0.4, 89, 0.03 0.8865 0.2487 0.2124

Lower Dubti 5-4-1 0.8953 0.2618 0.2531 0.4, 94, 0.07 0.8938 0.3094 0.2870Eliwuha 5-4-1 0.9122 0.2190 0.2015 0.5, 97, 0.06 0.9024 0.2100 0.1993Bati 6-4-1 0.9450 0.2236 0.2159 0.8, 98, 0.05 0.8953 0.2386 0.2114

12 Month lead timeUpper Bantu Liben 5-6-1 0.8372 0.3342 0.3025 0.55, 88, 0.08 0.8171 0.3531 0.3388

Ginchi 6-5-1 0.8637 0.3373 0.3191 0.65, 96, 0.08 0.8284 0.2743 0.2414Sebeta 5-5-1 0.8331 0.3325 0.3282 0.85, 99, 0.06 0.8398 0.3548 0.3302Ejersalele 8-6-1 0.8277 0.3372 0.3362 0.8, 88, 0.09 0.8420 0.3353 0.3209Ziquala 7-5-1 0.8316 0.3245 0.3083 0.6, 91, 0.06 0.8554 0.3560 0.3422

Middle Modjo 6-4-1 0.8419 0.3061 0.2931 0.6, 91, 0.05 0.8013 0.3591 0.3396Wolenchiti 8-5-1 0.8134 0.2948 0.2844 0.45, 100, 0.09 0.8400 0.3159 0.2760Gelemsso 7-6-1 0.8178 0.2879 0.2753 0.6, 98, 0.08 0.8223 0.2777 0.2697Dire Dawa 8-6-1 0.8659 0.2853 0.2762 0.65, 92, 0.05 0.8548 0.3410 0.3163

Lower Dubti 5-5-1 0.8303 0.2827 0.2749 0.5, 88, 0.09 0.8472 0.3051 0.2827Eliwuha 6-4-1 0.8462 0.2874 0.2697 0.25, 100, 0.1 0.8494 0.3184 0.3073Bati 8-4-1 0.8086 0.2819 0.2620 0.88, 95, 0.07 0.8538 0.3019 0.2794

A. Belayneh et al. / Journal of Hydrology 508 (2014) 418–429 425

ANN models. For forecasts of SPI 12 (6 months lead time) the re-sults are very similar across all stations. Fig. 6 shows the forecastresults of the Eliwuha station for SPI 12. The figure indicates thatthe WA-ANN forecasts closely mirror the observed results and donot underestimate extreme events of precipitation or drought.The model does not accurately depict the inception of the droughtperiod at the end of 1970. While the observed SPI series indicates a

slight drought, the forecasts indicate a moderate period ofprecipitation.

Fig. 7 is a scatter plot of the observed and predicted SPI valuesfrom the WA-ANN model. The figure shows that the points are clo-ser to the trend line and there are no points of significant overes-timation or underestimation. Fig. 8 illustrates the effects of theapproximation series on the SPI time series for the Eliwuha station.

Table 8Results for the calibration/training data set of the Eliwuha station (SPI 12, 6 monthslead time).

Model R2 RMSE MAE

ARIMA 0.5837 0.8903 0.8773ANN 0.7241 0.3348 0.3180SVR 0.7528 0.3062 0.2381WA-ANN 0.9335 0.2140 0.1906WA-SVR 0.8631 0.2481 0.2301

Fig. 3a. Autocorrelation of the SPI 12 time series for the Eliwuha station.

Fig. 3b. Partial autocorrelation of the SPI 12 time series for the Eiwuha station.

Fig. 4. Observed vs. predicted SPI 12 at Eliwuha station for the ANN model.

Fig. 5. Scatter plot for SPI values at Eliwuha station for the ANN model.

Fig. 6. Observed vs. predicted SPI at the Eliwuha station for the WA-ANN model.

Fig. 7. Scatter plot from WA-ANN forecasts of SPI 12 at the Eliwuha station.

Fig. 8. Time series showing the observed SPI values against the approximationseries after wavelet decomposition for the Eliwuha station.

426 A. Belayneh et al. / Journal of Hydrology 508 (2014) 418–429

This study found that the approximation series after waveletdecomposition is useful to use in forecasting SPI time series. Forthe model in Fig. 8, the approximation series is from wavelet

decomposition at level three. The approximation series closelymirrors the periods of precipitation and drought exhibited by theSPI series. This approximation time series was subsequently usedas an input in WA-ANN or WA-SVR models. As seen in Tables 3–6,the forecast results for WA-ANN and WA-SVR models are improvedcompared to models without any wavelet pre-processing.

5.4. SVR models

Fig. 9 illustrates the forecast results of the best proposed SVRmodel at the Eliwuha station. The SVR model had trouble predict-ing the inception of drought at the end of 1970. While the modeldoes accurately predict events of drought there seems to be a slighttime shift error. The predicted values are slightly lagged compared

Fig. 9. Observed vs. predicted SPI 12 from a SVR model at the Eliwuha Station.

Fig. 10. Scatter plot of SPI 12 values for a SVR model at the Eliwuha Station.

Fig. 11. Observed vs. predicted SPI 12 from a WA-SVR model at the Eliwuha Station.

A. Belayneh et al. / Journal of Hydrology 508 (2014) 418–429 427

to the observed values, which may make applications of SVRmodels for drought forecasting problematic. The SVR model alsohad a good correlation between the observed and predicted valuesas exhibited by the R2 value of 0.7382. The scatter plot in Fig. 10illustrates the correlation between the observed and predictedSPI values. The observations in the scatter plot are symmetricalaround the trend line.

5.5. WA-SVR models

The use of wavelet analysis improved the forecasting ability ofSVR models with respect to SPI 12 and SPI 24. As shown in Tables4 and 6, the use of wavelet analysis improves the performancemeasures across all the stations. The R2 values for the WA-SVRmodels are between 0.8144 and 0.8968; these values are all greaterthan any SVR model for SPI 12, indicating a greater level of corre-lation between observed and predicted values. For forecasts of12 months lead time for both SPI values refer to Tables 3–6. Aswith other models an increase in lead time results in a deteriora-tion of the forecast accuracy.

The forecast results from WA-SVR models are more accuratethan SVR models, according to the performance measures. The in-puts for the WA-SVR models were generated from the approxima-tion series after wavelet decomposition of the SPI time series. Thefact that the use of just the approximation series improved theresults significantly indicates that the approximation series

adequately de-noises the data and avoids any discontinuities with-in the SPI time series.

Fig. 11 indicates that the WA-SVR model at the Eliwuha stationis good at predicting the inception of a drought as shown in the fig-ure around the end of 1970. Fig. 11 also indicates that the WA-SVRmodel tends to overestimate periods of extreme precipitation ordrought. The overestimation is not a mis-categorization of theevent. SPI values of �2 and �3 are both representative of extremeevents. In general, the predicted values mirror the trends observedwith the original time series. For the Eliwuha station, the WA-SVRmodel is effective at predicting the end of the SPI time series. Theresults from Figs. 6 and 9 show the models predicting slight tomoderate drought while the observed time series indicates slightprecipitation. The WA-SVR model was better at predicting theevents at the end of the time series. The scatter plot in Fig. 12shows the good level of correlation between the observed and pre-dicted SPI values at the Eliwuha station.

6. Discussion

This study has shown that data driven models can be an effec-tive means of forecasting drought at forecast lead times of 6 and12 months in the Awash River Basin. The results indicate that ma-chine learning techniques (ANNs and SVR) are more effective thana traditional stochastic model such as an ARIMA model in forecast-ing SPI 12 and SPI 24 at the aforementioned lead times. This islikely due to the fact that ANN and SVR models are effective inmodeling non-linear components of time series data. Furthermore,the use of wavelet analysis as a pre-processing tool improved theforecast results for both ANN and SVR models. As might be ex-pected, the results also indicate that as the forecast lead time is in-creased the correlation between observed and predicted values, asmeasured by R2, decreases considerably. While the RMSE and theMAE increase with increasing forecast lead time, their increase isnot as pronounced. An increase in forecast lead time from 6 to12 months did not result in poor results, especially when waveletanalysis was used, which highlights the effectiveness of this pre-processing method for ANN and SVR models in predicting theSPI. The input structure of the models does not change with the in-crease of forecast lead time, which makes the models convenientfor operational purposes.

The results from all the data driven models generally show thatSPI 24 forecasts were more accurate than SPI 12 forecasts. Both SPI12 and SPI 24 are long-term SPI and each new month has less im-pact on the period of sum precipitation (McKee et al., 1993) com-pared to short-term precipitation. As a result, monthly variation inprecipitation has a smaller impact for both these SPI compared toshort-term SPI. However, as SPI 24 is a longer term SPI its sensitiv-ity to changes in precipitation within the time series is less thanthat of SPI 12. This lack of sensitivity may explain why the modelsare slightly more effective at generalizing SPI 24 better than SPI 12.

Fig. 12. Scatter plot from WA-SVR forecasts of SPI 12 at the Eliwuha station.

428 A. Belayneh et al. / Journal of Hydrology 508 (2014) 418–429

The forecast accuracy of the proposed models does not differsignificantly between each of the basins. The lack of a significantdifference in terms of the forecast accuracy indicates that the dif-ferent conditions within the three sub-basins do not appreciablyaffect the forecast of the SPI. In general, the performances of SVRand ANN models were comparable. The use of wavelets improvedthe results of both machine learning techniques, with the forecastmeasures indicating that WA-ANN models slightly outperformedWA-SVR models. Theoretically, SVR models should perform betterthan ANN models because they adhere to the structural risk mini-mization principle instead of the empirical risk minimization prin-ciple. They should, in theory, not be as susceptible to local minimaor maxima. However, there have been studies that have shownthat the performance of SVR and ANN models are comparable.Lima et al. (2013) found that SVR models were more effective atprecipitation forecasts when MAE was the performance measureand ANN models were more effective when MSE was the perfor-mance measure. A study by Shin et al. (2005) and Chevalier et al.(2011) found that the application of ANN models in time seriesforecasting was comparable to those of SVR models especially asthe size of the training set was increased. The study by Chevalieret al. (2011) also found that SVR models were superior in the train-ing phase, while ANN models were superior in the evaluationphase. Witten et al. (2011) found that ANN models are comparableto SVR models because they can learn to ignore irrelevant attri-butes. Witten et al. (2011) also state that there is no universallysuperior learning method.

From the figures illustrating all the forecasts using all of thedata driven models, it is apparent that there is not much time steperror in the forecasts of SPI 12. However, the SVR model at the Eli-wuha station for SPI 12 did show a lag between observed and pre-dicted events. This time shift error is unique to the SVR models inthis study. This time shift error associated with the SVR models isindicated by the delayed drought forecasts. Time shift error iscaused by the autoregressive components related to the selectionof input variables (Abrahart et al., 2007). The use of past data inthe forecasts of SPI values at long lead times introduces time shifterror. Long lead time forecasts that do not possess time shift errorusually result in noisier forecasts (Chua and Wong, 2011). In anoperational setting, the presence of a time shift error would likelycompromise the ability of planners to implement an effectivedrought warning system. Forecasts of SPI 12 at the Eliwuha station

using the SVR model showed that the inception of the drought(according to the observed time series) was not accurately pre-dicted. However, the WA-SVR model at the same station did ade-quately predict the inception of drought but was relativelynoisier than the SVR model.

7. Conclusion

This study investigated the ability of data driven models to fore-cast drought. This study also proposed and evaluated, for the firsttime, the use of the WA-SVR method for long-term droughtforecasting.

Overall, coupled wavelet-neural network (WA-ANN) modelswere found to provide better results than the other model typesused for forecasts of SPI 12 and SPI 24 in the Awash River Basin,especially for SPI 24. WA-ANN models showed a higher coefficientof determination between observed and predicted SPI, as well aslower RMSE and MAE values compared to simple ANNs, ARIMA,SVR and WA-SVR models. Wavelet coupled models also consis-tently showed lower values of RMSE and MAE compared to theother data driven models. The coupled models provide more accu-rate results because pre-processing the original SPI time serieswith wavelet decompositions improves the forecast results overtime series that do not use wavelet decompositions. Wavelet anal-ysis de-noises the SPI time series and subsequently allows the ANNand SVR model to model the main signal without the noise. Wave-let analysis also reduces the sensitivity to changes in monthly pre-cipitation within the SPI time series. In the case of SVR models, theuse of wavelets also reduces the lag between forecasts and the ob-served SPI values.

This study focused on long-term drought forecasts of SPI 12 andSPI 24 in the Awash River Basin. Further studies need to be done todetermine which of these data driven models is suitable for fore-casting long-term SPI values in other locations with different cli-mates and different physical characteristics. Considering the factthat the Middle and Lower Awash sub-basins have a very similarclimate, studies of areas with different climates should be con-ducted to determine whether there is a significant link betweenforecast accuracy and climate. This study found that the differentcharacteristics and climatology of the sub-basins had no discern-ible effect on forecast accuracy. Future studies should also attemptto couple data driven drought forecasting models with uncertaintyanalysis, such as bootstrapping or boosting ensembles.

Acknowledgements

This research was funded by an NSERC Discovery Grant and aCFI Grant held by Jan Adamowski. The data was obtained from Na-tional Meteorological Agency of Ethiopia. Their help is greatlyappreciated.

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